You can try something like this without importing any module :
s1='appleandgold'
s2='appleblue'
track=[]
for k in range(len(s1)):
if k!=0:
for ka in range(0,len(s1),k):
if s1[ka:ka+k] in s2:
track.append((len(s1[ka:ka+k]),s1[ka:ka+k]))
print(max(track)[1])
output:
apple
solved String intersection in Python